Chapter 36
Image Formation 2
1. Thin Lens
2. Multi lens/mirror system
Thin lenses Lenses are commonly used to form
images by refraction. We discuss about spherical lenses only.
They are part of two spheres. There are two types of lenses
Converging Diverging
When the thickness of the lens is negligible, the lens is called thin lens.
Principal axis: the line that goes through the two centers of the two spheres.
Paraxial rays are those close to the principal axis.
Lenses are used in optical instruments Cameras Telescopes Microscopes
converging
diverging
Principal axis
Principal axis
Converging and diverging Lens Shapes
Converging: positive focal lengths thickest in the middle
Diverging: negative focal lengths thickest at the edges
Focal Length of a Converging Lens
The parallel rays pass through the lens and converge at the focal point
The parallel rays can come from the left or right of the lens
Focal Length of a Diverging Lens
The parallel rays diverge after passing through the diverging lens
The focal point is the point where the rays appear to have originated
Notes on Focal Length and Focal Point of a Thin Lens
Because light can travel in either direction through a lens, each lens has two focal points One focal point is for light passing in one direction
through the lens and one is for light traveling in the opposite direction
However, there is only one focal length Each focal point is located the same distance
from the lens
Ray Diagrams for Thin Lenses – converging
Ray diagrams are convenient for locating the images formed by thin lenses or systems of lenses
For a converging lens, the following three rays are drawn: Ray 1 is drawn parallel to the principal axis and then passes
through the focal point on the back side of the lens Ray 2 is drawn through the center of the lens and continues in
a straight line Ray 3 is drawn through the focal point on the front of the lens
(or as if coming from the focal point if p < ƒ) and emerges from the lens parallel to the principal axis
The image is real The image is inverted The image is on the
back side of the lens
PLAY
ACTIVE FIGURE
The 3-ray diagram again
Ray 1:Parallel to axis, then passes through far focal point
Ray 2:Passes unchanged through center of lens
Ray 3:Passes through near focal point, then parallel to axis
F
F
fObject
hodo
Real image, inverted, smaller
hi
di
o
i
o
i
d
d
h
hm :ionmagnificat
Object distance, 5 cases: 1 -- 2
FF
f2f
Real, inverted, smaller
FF
f2f
Real, inverted, same size
FF
f2f
Real, inverted, larger
FF
f2f No image
Object distance, 5 cases: 3 -- 4
FF
f2f
Virtual, upright,larger
Like in the converging mirror case, there are 5 possible object locations that produce different images.
While in the diverging lens case, like in the diverging mirror case, no matter where the object is placed, you always get a virtual, upright and smaller image.
Object distance, 5 cases: 5
Ray Diagrams for Thin Lenses – Diverging
For a diverging lens, the following three rays are drawn: Ray 1 is drawn parallel to the principal axis and emerges
directed away from the focal point on the front side of the lens Ray 2 is drawn through the center of the lens and continues in
a straight line Ray 3 is drawn in the direction toward the focal point on the
back side of the lens and emerges from the lens parallel to the principal axis
The image is virtualThe image is uprightThe image is smallerThe image is on the front side of the lens
The 3-ray diagram againRay 1Parallel to axis, virtual ray passes through near focal point
Ray 2Straight through center of lens
Ray 3Virtual ray through far focal point, virtual ray parallel to axis
F
Ff
Object
hodo
Virtual image, upright, smaller
hi
di
The Camera
The photographic camera is a simple optical instrument
Components Light-tight chamber Converging lens
Produces a real image Film behind the lens
Receives the image
The Eye
The normal eye focuses light and produces a sharp image
Essential parts of the eye: Cornea – light passes
through this transparent structure
Aqueous Humor – clear liquid behind the cornea
The Eye – Close-up of the Cornea
Combinations of Thin Lenses
The image formed by the first lens is located as though the second lens were not present
Then a ray diagram is drawn for the second lens
The image of the first lens is treated as the object of the second lens
The image formed by the second lens is the final image of the system
Combination of Thin Lenses, example